# Tutor profile: Philip N.

## Questions

### Subject: Applied Mathematics

The previous one was basically applied math since I could not draw out the trigonometry problem, but herewith another one: If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?

If the car travels 72 000m per hour, then it means that the car travels: per minute = per hour/60 per minute = 72 000 / 60 per minute = 1200m We have been told that the tire rotates 400 times per minute thus: 400x = 1200 x = 3m

### Subject: Trigonometry

Frank flies a kite with a string length of 25 m and at an incline of 65°. What is the height of the kite above ground? What is the horizontal distance from Frank to the kite?

We are working with a right angle here so we can apply the trigonometric ratios for right angled triangles here: sinx = opposite / hypotenuse cosx = adjacent / hypotenuse tanx = opposite / adjacent We have the hypotenuse length (25m) and the angle between the horizontal line (lets call it "d") and the hypotenuse. Thus in order to determine the height (h) we can use the sinx equation above since h will be opposite the angle that is known. Thus: sin65 = h/25 h = 25sin65 h = 20,7 m To answer the next question we can either use Pythagoras or one f the trigonometric ratios for right angled triangles. Lets use Pythagoras for some diversity: Assume the hypotenuse length is represented by "y" Thus y^2 = h^2 + d^2 (25)^2 = (20,7)^2 + d^2 d^2 = 625 - 428,49 d^2 = 196,51 d = sqrt(196,51) d = 14,02 m

### Subject: Algebra

Provide the solution to the system of linear equations given below: x - 7y = 23 ; 4x - 3y = 42

Step one: Solve x for the first equation x = 23 + 7y Step 2: Now replace x in the second equation with the solution above 4(23 +7y) - 3y = 42 92 + 28y - 3y = 42 25y = 42 - 92 25y = -50 y = -2 Step 3: Calculate the value for x by substituting the value for y into the first equation: x = 23 + 7(-2) x = 23 - 14 x = 9 Thus x = 9 and y = -2

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